d/(dy)((1/(y^2)-5/(y^4))(y+7y^3))

Lösung

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))

\frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

Schritte zur Lösung

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{y ^{2}} - \frac{5}{y ^{4}}, g = y + 7 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}) + \frac{d}{d y} (y + 7 y^{3}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{20}{y ^{5}}

\frac{d}{d y} (y + 7 y^{3}) = 1 + 21 y^{2}

= (- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}})

Vereinfache

(- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) : \frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

= \frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

a re a x^{2} - 3 x, 2 x + 6

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